You can book for a bus ticket from Asian a or European side of Istanbul to Goreme. Bus will take you to Nevşehir city bus station and later they will get you to Goreme, Urgup, Avanos, Ucisar or Cavusin with shuttle. Bus ride takes around 12 hours from Istanbul to Cappadocia (Goreme). This can provide you to make an over night bus ride and save the day for wandering around.
You can fly from Istanbul to Cappadocia Airport which is in Gulsehir. It is 45 min away grom the hotels zone. In Istanbul you have two options for airport: Istanbul Airport which is in European side, Sabiha Gökçen Airport which is in Asian side. Cappadocia Air port is a small airport and there is no public bus from air port to hotels zone. You can check for shuttle companies on LocalCappadocia and book for your shuttle. You can book for the shuttle for your arrival and departure. They will pick you from the air port and transfer to your hotels doorstep and at your departure from hotel to airport. There is also an other airport 1 hour away from the hotels zone: Kayseri Airport. Finding flight to Kayseri Airport is rather easier and can be even cheaper. Most busy flights from Istanbul to Kayseri is from Sabiha Gökçen Airport. Still you can check for the shuttle transfer from Kayseri Airport to your hotel.